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Question

Find component of vector A along the direction of B A||B and in perpendicular direction of B AB.


A

A||B = 5; AB=53

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B

A||B = 53;AB=5

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C

A||B = -5; AB=53

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D

A||B = 53;AB=5

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Solution

The correct option is C

A||B = -5; AB=53


So component of A along direction of B is Acos120=Asin30=5

[cos(90+θ)=sinθ]

Here we can see if just measure the shadow you will get a cos60=a2=5

But since this 5 is in the opposite direction of vector B so we say that the component of A along the

direction B is -5.

Now component in the perpendicular direction of B is

Asin(120)=Acos30=53

[sin(90+θ)=cosθ]

Just the shadow measurement is a cos 30 and it's in the perpendicular direction, so no need to

change sign.

So component along the direction is always acosθ and in perpendicular direction is asinθ. This will take care of sign so don't worry.


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